This paper contrasts two information-theoretic approaches to statistical explanation: namely, (1) an analysis, which originated in my earlier research on problems of testing stochastic models of learning, based on an entropy-like measure of expected transmitted-information (and here referred to as the Expected-Information Model), and (2) the analysis, which was proposed by James Greeno (and which is closely related to Wesley Salmon's Statistical Relevance Model), based on the information-transmitted-by-a-system. The substantial differences between these analyses can be traced to the following basic (...) difference. On Greeno's view, the essence of explanation lies in the relevance relations expressed by the conditional probabilities that relate the explanans variables to the explanandum variables; on my view, in contrast, the essence of explanation lies in theories viewed as hypothetical structures which deductively entail conditional probability distributions linking the explanans variables and the explanandum variables. The explanatory power of a stochastic theory is identified with information (regarding the values of explanandum variables) which is "absorbed from" the explanans variables. While other information which is "absorbed from" the explanandum variables (through the process of parameter estimation, for example) reflects descriptive power of the theory. I prove that Greeno's measure of transmitted information is a limiting special case of the E-I model, but that the former, unlike the latter, makes no distinction between explanatory power and descriptive power. (shrink)

In his recent book Scientific Explanation and the Causal Structure of the World Wesley Salmon provides a detailed explication of objective homogeneity, a concept which is central to his Statistical-Relevance (S-R) model of explanation. One of the purposes of Salmon’s explication is to refute Hempel’s thesis of the epistemic relativity of statistical explanation. According to this thesis “the concept of statistical explanation for particular events is essentially relative to a given knowledge situation” (Hempel 1965, pp. 402-403, quoted in Salmon 1984, (...) p. 48). Salmon introduces (1984, p. 55) the concept that forms the basis for his S-R model as follows: “A reference class A is homogeneous with respect to an attribute B provided there is no set of properties Ci (1 ≤i ≤ k; k ≥ 2) in terms of which A can be relevantly partitioned. (shrink)